What is a Sentence?

I recall in second grade getting an answer wrong on a test. The question was, "Who is a carpenter?" and I replied,
"John's mother." I lost points, because "John's mother" was not a sentence; I should have written, "John's mother is a carpenter."
With that experience in mind, I will offer some guidelines to making sure you state your ideas in sentences. Let's begin with a rough definition:

A sentence is a purposeful sequence of words with a subject and a verb. Thus, the following is not a sentence:

The tree

Nor is the following:

Grows in the park

Both examples are sentence fragments— possible components of a sentence, but not sentences in themselves. Now look at this example:

The tree grows in the park.

This is a sentence, since it has a subject — the tree — and a verb — grows.

Okay, sure, but that's not the whole story. Consider these examples:

She rode her bike to class.

When she rode her bike to class.

Both have a subject— she— and a verb— rode— but only the first one is a sentence. The second is subordinated by the word when (more on that later). It cannot stand on its own, and so it is not a sentence, but a fragment.